Exploration of Layer Specific Dimensional Multipliers in Modified Unit Cell Synthesis Method Meta-Materials for Nonlinear Applications

Topology optimization of periodic metamaterials for structural applications usually results in uniformly distributed cells. This paper presents a novel concept designed to better tailor unit cell-based meta-material designs for nonlinear structural applications. First, previous work in the development of a systematic method for the construction and optimization of these advanced materials is reviewed. Results of a previous case study for the design of meta-material backer pads for the wheels of the Abrams tank are presented to provide a platform for the introduction of layer specific dimensional multipliers, dubbed “size factors”. These add an additional layer of complexity for the previously designed homogeneous materials. The methodology behind the size factors is presented and the implementation of the “size factors”, as it pertains to the meta-materials designed using the Modified Unit Cell Synthesis method, is then discussed. Initial assumptions for a final size factor arrangement are presented, prompting the creation of two optimization procedures to compare against one another. Results for both optimizations are obtained and while both show an increase in nonlinearity over the original material, the unorganized arrangement of the parameters results in the most optimal designs, with near zero error between the target and obtained non-linear force-strain relationships.